Console disconnects when a game is started

My console will connect to Xbox live when I start it and log in, but when I start a game from the dashboard it disconnects from live and i cant reconnect. when i try to test my connection all it says is that I need to restart my router which is not my problem
because i have tried that multiple times with no avail. This started when i tried to download the latest Call of Duty: Black Ops update and it wouldn't download. so i tried again later and it wouldn't even bring the update up I would just get disconnected
form Xbox Live. Is there any way that I can fix this?

Try clearing you Xbox Cache, by going to system setting and then memory. Also please make sure with the game your trying to play online is updated. For example a message may come up saying "Download this update to connect to XBL and play online".